Potentiometer



J. CLAYTON, JR

POTENTIOMETER Oct. 5, 1965 FiledApril 18, 1963 2 Sheets-Sheet 1 lllllllllllllllllllllIllllllll INVENTOR.

Oct. 5, 1965 J. CLAYTON, JR

POTENTIOMETER 2 Sheets-Sheet 2 Filed April 18, 1963 United States Patent O 3,210,711 v POTENTIOMETER John Clayton, Jr., Maynard, Mass., assignor to Waters Manufacturing, Inc., Wayland, Mass., a corporation of Massachusetts Filed Apr. 18, 1963, Ser. No. 274,390 13 Claims. (Cl. 338-175) This is a continuation-in-part of application Serial No. 98,257, iiled March 24, 1961, now abandoned.

This invention relates to an improved construction for a potentiometer and more particularly for a rotary potentiometer in which the distance between the axis of rotation of the brush and the resistance element varies, with the angular position of the brush. The instant invention also provides .an improved construction for taps on a resistance element consisting of two or more separate portions.

A conventional rotary potentiometer has its resistor spaced a uniform distance from the axis of movement of its brush. However, in certain specific applications, such as function generation, it is desirable to have a varying distance between the axis of movement of the brush `land the resistor, thereby varying the rate of change of that in precision potentiometers a difference in contact force is very undesirable, since the lightest force consistent with the conditions of use is desirable in preventing Wear, so that a distance variation of this type is found to produce limits on performance obtainable with usual constructions, if of the order of ten percent or more, las in the case, for example, of a resistance element disposed about the rotational axis in the form `of a square.

It is accordingly an object of the instant invention to provide an improved construction in which variation of contact force between a wiper and a resistor is minimized although the distance between the resistor and the axis of rot-ation of the wiper varies relative to the angular position of the wiper about its axis.

In the potentiometer to be described herein, the resistance element is in the form of a square, in order that the output voltage at the brush be a particular function of angular position. The element is provided with taps at the corners of the square. Such a potentiometer is conveniently constructed by employing separate mandrels or cards for the sides Iof the square. The present invention provides a novel form of combined interconnection and tap for such a potentiometer.

It is a further object of the present invention to provide an improved construction for a precision potentiometer which may be economically. and eiiciently assembled without diminishing the precision of the potentiometer.

Other objects and advantages of the invention will become readily apparent to those skilled in the art upon description of the embodiments of the accompanying drawing in which:

FIGURE 1 is a plan View of a potentiometer embodying the instant invention with the cover thereof shown in section for clarity of illustration;

FIGURE 2 is a rear view of the potentiometer shown in FIGURE 1;

FIGURE 3 is a cross-sectional view taken on offset line 3-3 of FIGURE 1 but illustrating the brush assembly shown therein as rotated by 45 degrees in the direction of resilient finger 60 with respect to the position of FIGURE l;

FIGURE 4 is an exploded perspective view showing the assembly of a brush and a shaft of the potentiometer shown in FIGURE l;

FIGURE 5 is an enlarged fragment of a portion of a pair of separate resistance elements of the potentiometer forming a corner and showing a portion of a terminal assembly in contact with the resistance elements;

FIGURE 6 is a sectional view along line 6 6 of FIG- URE l;

FIGURE 7 is a fragmentary view similar to FIGURE 5, but illustrating a modified form of the potentiometer;

FIGURE 8 is a view in perspective of the portion of the potentiometer illustrated in FIGURE 7; and

FIGURE 9 is a schematic composite illustration, the upper portion being a fragmentary electric circuit diagram of the portion of the potentiometer illustrated in FIGURES 7 and 8, with the addition of the wiper, and the lower portion illustrating in highly schematic form the potential appearing on the Wiper as a function of its position as the wiper is moved along the vertically corresponding regions of the resistance element construction, the solid curves illustrating normal operation and the dotted curves illustrating operation in the event of development of certain defects.

Referring now to FIGURES 1 through 6 of the drawing, it may be seen that the potentiometer 10 therein illustrated generally consists of a molded dielectric base 12, a resistor 14 mounted on said base, a shaft 16 rotatably mounted in the base, a brush 18 mounted on the shaft and electrically contacting the resistor, and a cover 20 mounted on the base and enclosing the resistor and brush and having the shaft 16 protruding therefrom.

Base 12 has an integral inner boss 22. A bushing 24 is molded into said base within the boss 22. The base has a slip ring recess 26 on the rear side. A radial slip ring terminal groove 28 lopens into the recess 26 for reasons which will become apparent hereinafter. In addition to the slip ring terminal groove, the base has four resistor terminal grooves, 30, 32, 34 and 36, equiangularly spaced from each other and extending radially outward from the center of the base. On the same side as the grooves, there are molded in the base three threaded inserts 38 which provide a convenient means for mounting the potentiometer.

On the inner or front side of the base are resistance element grooves 40, 42, 44 and 46. These grooves form a square. Each groove has a plurality of enlargements 48 for reasons which will become apparent hereinafter. Inwardly adjacent to each corner of the square is a rivet aperture 50 which extends through the base and opens onto one of the terminal grooves.

The resistor consists of four identical resistance elements each of which consists of a resistance Wire wound on a card. A resistance element 52 is positioned in groove 40 and resistance elements 54, 56 and S8 are positioned in grooves 42, 44 and 46 respectively. The resistance elements are held in place by a suitable cement. It may be noted that the enlarged portions 48 of the various grooves provide a space for receiving cement.

Adjacent ends of the resistance elements are connected to each other by a resilient finger or prong. As may be seen in FIGURE 5, a resilient linger 60 connects the resistance elements 54 and 56. The resilient iinger includes an apertured hub 62 and a prong 64 which electrically contacts the ends of the resistance elements 54 and 56. The resilient nger 60 is xed to the base by means of a rivet 66 which extends through one of the openings 50 and is fixed to a terminal lead 68 which is positioned in terminal groove 36. Similar assemblies at the other corners consist of finger 70, rivet 72 and terminal 74, finger 76, rivet 78, and terminal 80, and finger 82, rivet 86, and terminal 84. The terminals are further secured to the base by a cement which covers the ends of the terminals in contact withthe respective rivets.

As was mentioned above, the shaft 16 is rotatably mounted in the base. The shaft, which is an electrical conductor, has an integral shaft head 88 which contains a slot 90. A terminal 92 with an'intcgral ring is positioned in slip ring recess 26 and slip ring terminal groove 28. The shaft rotatably passes through the terminal and a spring washer 94 is positioned between head 88 and the ring to assure firm electrical connection. The shaft has on its outer end an annular groove 96 which receives the brush 18. A second spring washer 98 is positioned between the boss 22 and the brush 18 to secure to the shaft in longitudinal position.

The brush 18 includes a a ybrush arm mount 100 which consists of a clamp 102 and a tab 104 integral with the clamp, this mount being, for example, of the type sold commercially as a Truarc washer. The clamp is mounted in a groove 96 to secure the brush to the shaft and to connect the clamp to the shaft electrically. A resilient arm 106, which is a portion of the brush, is xed to the tab 104. The resilient arm comprises a substantially circular portion 107 which surrounds boss 22 and has an enlargement 108 on one side which is fixed to tab 104. On the other side of the arm and at 180 degrees from the mounting is a wiper 110, bent to V-shape crosssection and thus comparatively rigid, although formed as an integral portion of resilient arm 106. The portion 108 of the resilient arm is spot welded to the tab 104 so that there is an electrical contact between the mount and the resilient arm and wiper, and the resilient arm and the brush arm mount define an acute angle so that the resilient arm extends slightly downward from the tab to slidingly vengage the resistance element.

The base 12 has a shoulder 112 which receives the side wall 114 of the cover. The face 116 of the cover has a shaft aperture 118 at its center through which protrudes,

with substantial clearance, the end of shaft 16, having an operating slot 120.

It will be seen upon study that the construction described produces relatively uniform contacting force between the wiper and the resistor irrespective of the angular position of the brush. As is evident from FIG- URE 1, when the wiper is perpendicular to one of the resistance elements, the distance between the shaft and the resistance element is at a minimum. However, when the shaft is rotated 45 degrees, the wiper then contacts the resistor at a maximum distance from the axis of rotation of the brush and a different portion of the wiper engages the resistor. The distance of the contact point from the rotational axis thus varies by a substantial fraction of the maximum distance, and the radial length of the contacting surface of the wiper of course corresponds to this variation. inasmuch as the contacting force is determined by the resilience of the resilient arm of the brush, it is obvious that although different points on the wiper contact the resistor, variance of contacting force is greatly reduced as compared with conventional constructions inasmuch as the wiper is a relatively long distance from the point where the annular resilient arm is fixed to the tab of the brush arm, the latter point being, as seen in the drawing, spaced from the axis by a distance greater than the radial length of the contacting surface of the wiper.

' Also, it will be seen that the slight downward tilt of the contacting end portion of the wiper, i.e., the fact that the outer end of the contacting portion is axially beyond the plane of contact in the direction of resilient urging, while the inner end is axially short of the plane of contact in this direction, produces the result of decreasing the stressing of the resilient support element in the regions of smallest distance from the shaft where contact force would be largest were the stressing of the support element to remain completely constant. This tilt, i.e., the disposition of the generally radially extending substantially rigid contacting portion of the wiper at an angle to the plane of contact carrying the joint between the contacting portion and the resilient support portion in the axial direction which increases the stressing of the resilient portion with increasing distance of the contact point from the axis, constitutes a means for varying the stressing of the resilient support to compensate for the distance variation which tends further to hold the contact pressure constant. The direction of tilt is for this purpose such that the radially inward part of the contacting portion of the wiper is displaced from the plane of contact in the axial direction which reduces the stressing or contact pressure as compared with that which would be produced if the contacting portion were in, rather than intersecting, the plane of contact. It will be observed that this feature of construction produces slight bending back and forth of the resilient support as the shaft is rotated; any effects of fatigue so produced are, however, reduced by the lengthening of the resilient support produced by the location of its rigidly mounted inner end, as previously described. Thus, the potentiometer diameter over-all may be kept relatively small but the effect of varying of contact force between the wiper and the resistor is kept to a minimum.

The potentiometer of FIGURES 1 through 6 has, in addition to the provision of a simple and inexpensive solution for the problem of contact variation, as described above, further features of construction making manufacture very simple and inexpensive while at the same time preserving the full precision and accuracy required. The structure in which the resilient finger 60 effects the connection between the ends of the elements S4 and 56 (with similar construction at the other corners, as indicated above) and at the same time serves as the exterior connection terminal, all by the single operation of installation of a rivet, obviously adds greatly to the economy of construction by eliminating a number of assembly operations. In addition, however, this construction serves the important function of winding control. With the illustrated construction, it .becomes unnecessary to maintain great precision in having on each of the four side elements exactly the same number of windings of the very tine wire which is of course used. It is relatively easy to maintain highly accurate dimension control on the simple parts other than the wound resistance elements, as compared with controlling the number of turns with great precision in the making of each element, or accurately tapping in near the ends by conventional methods such as spot-welding terminating leads. Where terminating leadsare used, locating them at the proper points to produce equal resistance in all arms, and also to produce substantial symmetry of position of the small regions of angular travel in which the wiper proceeds from an end of one element to the adjacent end of the next, is very difcult.

The use of the illustrated biting engagement of the corners of the lug 60 with the resistance elements at points slightly spaced from the ends, as best seen in FIGURE 5, solves all of these problems simultaneously, making it unnecessary to wind all the elements precisely and completely identically, while at the same time making it unnecessary to either perform any operation of joining leads to the tap points or to perform the even more difficult operation of exactly locating such tapped points which exists where conventional connections are used, the mere placing of the hub 62 of the finger or lug in appropriate posi-k tion automatically assuring tapping at the proper positions on the adjacent elements to produce uniformity of vall arms in the completed assembly.

In FIGURES 7 and 8 is shown a modified form of thel corner construction justV discussed. As before, the resistance elements, here designated as 154 and 156, are again connected by a resilient finger 160 having a hub 162 and a prong 164, the latter being formed with corners biting into the resistance wires to perform the same functions as previously described, connecting the ends of the active regions of the resistance elements so dened-to a rivet 166, again serving as the connection to an external terminal 168 (illustrated only in FIGURE 9, to be described later). The extreme end portions 170 and 172 of the elements 154 and 156 are again rendered electrically inert or unused by this connection or tap. Here, however, the extreme ends of the resistance wires themselves, shown at 174 and 176, serve as additional leads soldered or spotwelded to the assembly of the linger and rivet.

This construction is particularly desirable in applications where, as is quite frequent, any complete failure of such a potentiometer is intolerable, but it is satisfactory to provide, for the event of any failure, an emergency mode of operation producing only a slight impairment of overall precision. The finger or joint illustrated in connection with FIGURE 5 is for most purposes completely satisfactory. However, under extreme conditions of vibration, exposure to corrosion or dirt, and similar types of undesirable environmental conditions, one of the biting corners of the prong 64 (164 in FIGURES 7 and 8) may lose the desired completely conductive engagement more readily than a welded or similarly secured joint. In such an application as, for example, use in a navigational instrument, such loss of contact would frequently render the entire instrument employing this function potentiometer inoperative.

The construction of FIGURES 7 and 8 permits the realization of the economies inherent in the construction of FIGURE 5 even in cases where such a Contact failure as just described might at first appear to make it necessary to sacrifice the economy for complete assurance against catastrophe. The illustrated construction in essence provides a standby connection which normally has no effect whatever on the operation of the potentiometer, but which gives, in the event of the otherwise catastrophic occurrence of opening of one or both of the biting mechanical contacts, an emergency interconnection between the parts which keeps the potentiometer fully operative for its intended purpose, with only an extremely slight decrease in accuracy, which is readily acceptable for emergency use even though losing the full precision normally desired.

The manner in which this is accomplished by the structure of FIGURES 7 and 8 is best seen in FIGURE 9. In the upper portion of this gure, there is illustrated in electrical schematic form the circuit of the structure just described, with the wiper 1t) added. As will be there seen, the prong 164 shorts the ends 170 and 172 of the elements 154 and 156, but in the event of failure of the connection of the prong at either end, the effect is the addition of the relatively small number of turns previously unused.

g The lower portion of FIGURE 9 shows the overall eect of this. The solid portions of the curve show the usual or normal potential pattern on the wiper. It will be understood that this illustration is highly qualitative, certain features of the illustrated curves being greatly exaggerated for purposes of understanding. In the example selected for illustration, the right hand end of the element 156 (not shown) is connected to a negative potential, the left hand end of the element 154 (not shown) is connected to a positive potential, and the terminal 168 is grounded or neutral. As indicated above, it will readily be recognized that this illustrative example is not actually a generally typical use of such potentiometers, which are normally employed with quadrature alternating voltages and other system signals, but the simple example serving in full the purposes of the present discussion. The curves 178 and 179 show the normal voltage pattern as a function of angular position of the wiper 10 as it goes through the joint, the curve 178 reaching the zero voltage value at and the curve 179 reaching the zero voltage value at 182, these being the positions corresponding to the connections of the prong 164 above. The intermediate region is of course one of constant zero potential. The dotted curves 184 and 186 represent the shifted curves which occur in the event of opening of respective mechanical contacts of the prong 160. As will be seen, a slight shift is produced in the voltage versus position characteristic, but as will be seen by the convergence (more or less exaggerated) of the respective solid and dotted lines, the error introduced diminishes, of course, with increase of distance of the wiper from the joint.

As previously indicated, the structure accordingly obtains the full advantage of the economies inherent in the type of winding control shown in FIGURE 5, while at the same time providing a safety or standby type of operation which is fully satisfactory as an emergency measure for most applications, in the event of any failure.

Although the present potentiometer is one which has a square resistor, it is obvious that the present construction is desirable with resistors which are triangular, pentagonal, etc., and that some of the features are adaptable even to resistance elements of conventional shape. Accordingly it will be obvious that various uses and modifications of the instant invention may be made by those skilled in the art without departing from the spirit and scope of the invention. It will thus be understood that the patent protection to be afforded to the present invention should be limited in scope only by the appended claims and reasonable equivalents.

What is claimed is:

1. In a potentiometer, a rotatably mounted shaft bearing a brush assembly, and a resistance element supported in spaced relation to the shaft in the path of rotation of the brush assembly and contacted by the brush assembly at successive points all spaced from the shaft in a direction perpendicular to the shaft by a distance varying with shaft rotation, the distance variation being a substantial fraction of the maximum distance, said brush assembly comprising a unitary resilient arm having one end portion comprising a resistance-contacting surface having a single contacting region at each radial distance from the shaft and of radial dimension at least equal to said distance variation contacting said resistance element at points on said surface determined solely by distance of the contacted portions of the resistance element from the shaft, and the other end portion mounted on the shaft for rotation therewith wholly at a position spaced from the axis of the shaft in the direction generally opposite from the contacting end portion by a distance greater than said radial dimension of the resistance-contacting surface, so that variation of contact pressure with distance of the contact point from the shaft is minimized.

2. The improved construction of claim 1 wherein the portion of the arm intermediate to the mounted end portion and the contacting end portion comprises a ring surrounding the shaft in spaced relation thereto.

3. The improved construction of claim 2 wherein the contacting end portion comprises a flat strip bent to the form of a V and extending from the ring.

4. In a potentiometer having a base and a resistor mounted on one side of the base, the resistor being of a shape including a sharp angle, the improved construction wherein the resistor comprises two separate resistance elements with adjacent ends, arranged at a sharp angle with respect to each other, and having a resilient conducting nger on the base at the angle, the nger having sharp contacting portions in biting engagement with each of the adjacent resistance elements ends and forming a joint therebetween and constituting the sole electrical connection therebetween.

5. The improved construction of claim 4 having a conductive fastener member extending through the base and a tap terminal on the opposite side of the base, the fastener member engaging the finger and the terminal to simultaneously secure the finger in position to connect the resistence elements and electrically connected the joint between the elements to the tap terminal.

6. A potentiometer comprising, in combination, a base, a resistance element mounted on said base, a second resistance element mounted on said base having one end adjacent to one end of the first-mentioned resistance element, a resilient conductive finger mounted on the base adjacent to said ends of said resistance elements, said iinger having sharp contacting portions in biting engagement with each ofthe resistance elements and electrically contacting the ends of said elements, a terminal mounted on said base being electrically connected to said finger, a shaft rotatably mounted in said base, a tab mounted on said shaft, and extending radially therefrom, a resilient arm having one portion secured to said tab, said resilient arm having a length greater than said tab and forming an acute angle with said tab, and a wiper mounted on said resilient arm on a portion opposite that secured to said tab, said wiper being engageable with the resistance elements for electrical contact therewith.

7. A potentiometer comprising, in combination, a dielectric base, said base having a resistor groove defining a substantially closed figure and a plurality of adhesive recesses associated with said groove, a resistor mounted in said groove and secured to said base by an adhesive in said adhesive recesses, said resistor including a plurality of resistance elements, each of said resistance elements having one end adjacent to an end of an adjacent resistance element, a resilient conductive finger mounted on said base adjacent to each pair of ends lof the resistance elements, said finger having sharp contacting portions in biting engagement with each of the resistance elements and electrically contacting the said ends of said resistance elements, said base having a plurality of terminal grooves on the side opposite the resistor groove, each of said resilient fingers being electrically connected to a terminal positioned in a terminal groove, said terminals being secured to said base by an adhesive, an electrically conductive shaft rotatably mounted in said base within the figure defined by the resistor groove, a clamp mounted on said shaft for rotation with said shaft, a tab fixed to said clamp and being electrically connected thereto, an annular resilient arm mounted on said tab and being electrically connected thereto, said annular resilient arm encircling the shaft, a wiper fixed to said arm and being electrically connected thereto at a position opposite the position of mounting of the arm on the tab, said wiper being in electrical contact with the resistor, a shaft terminal electrically connected to the shaft and being positioned in one of said terminal grooves, and a cover mounted on said base to enclose the brush and the resistor.

8. In a potentiometer, a rotatably mounted shaft, a brush assembly mounted on the shaft, a resistance element supported in spaced relation to the shaft in the path of rotation of the brush assembly, said brush assembly comprising a wiper and spring means urging the wiper axially into contact with the resistance element at points of successive contact all spaced from the shaft in a direction perpendicular to the shaft axis by a distance varying with shaft rotation, the distance variation being a substantial fraction of the maximum distance, the wiper being a substantially rigid member having a contacting portion having a single contacting region at each radial distance from the shaft and of radial length at least equal to the maximum distance variation, the contacting portion being disposed at an acute angle to the plane of contact, the wiper moving in the direction parallel to the axis of the shaft to increase the stressing of the spring means as distance of the contact point from the shaft is increased, said spring means comprising an arm having the inner portion fixedly mounted with respect to the shaft at a point spaced from the shaft on the side opposite the wiper by a distance greater than the radial length of the contacting portion of the wiper, the outer portion supporting the wiper.

9. A potentiometer comprising a rotatably mounted shaft bearing a brush assembly, and a resistance element substantially entirely surrounding the shaft, supported in the path of rotation of the brush assembly and contacted by the brush assembly at successive points all spaced from the shaft in a direction perpendicular to the shaft by a distance varying with shaft rotation, the distance variation being a substantial fraction of the maximum distance, the brush assembly having a contact portion at the outer end having a single contacting region at each radial distance from the shaft and of a radial dimension substantially equal to said variation in distance, a rigid portion extending radially from the shaft at the inner end, and a resilient connecting portion rigidly secured to the rigid portion and the contact portion, said resilient connecting portion beingv connected to the rigid portion at a point spaced from the shaft on the side of the shaft opposite the contact portion by a distance greater than said variation in distance, the resilient connecting portion urging the contact portion against the resistance element, so that variation of contact pressure with distance of the contact point from the shaft as the shaft is rotated is minimized.

10. A potentiometer having (a) a base, i

(b) a plurality of separate wire-wound resistance elements on the base with mutually adjacent end portions,

(c) a wiper contact movable over the resistance elements,

(d) a resilient conducting member mounted on the base adjacent to each pair of adjacent end portions, said member having spaced wire-contacting portions each in biting engagement with the wire of a respective one of the adjacent resistance element end portions and forming a joint electrically interconnecting the adjacent elements,

(e) the wire windings of each of the adjacent elements extending beyond the points of such biting engagement toward the adjacent end portions but' being rendered inactive `in the operation of the potentiometer by such interconnection of adjacent elements,

so that the terminations of the active portions of the elements are substantially independent of small variations in number of wire windings and exact positioning thereof on the elements.

11. The potentiometer of claim 10 wherein said biting engagements of the conducting member constitute the sole electrical interconnection between the elements.

12. The potentiometer of claim 1t) wherein the ends of said adjacent resistance wire windings are electrically connected to the conducting member.

13. The potentiometer of claim 10 having (f) a conducting fastener securing the conducting member to the base and extending through the base for external electrical connection of the joint interconnecting the adjacent elements.

References Cited by the Examiner UNITED STATES PATENTS 988,456 4/11 Gernsback 338-89 X 2,081,227 5/ 37 DeVries 338-202 X 2,483,125 9/49 Cummerow et al 338-89 X 2,979,681 4/61 Brown 338-89 FOREIGN PATENTS 333,489 2/21 Germany.

409,379 4/ 34 Great Britain.

RICHARD M. WOOD, Primary Examiner.

ANTHONY BARTIS, Examiner. 

1. IN A POTENTIOMETER, A ROTATABLY MOUNTED SHAFT BEARING A BRUSH ASSEMBLY, AND A RESISTANCE ELEMENT SUPPORTED IN SPACED RELATION TO THE SHAFT IN THE PATH OF ROTATION OF THE BRUSH ASSEMBLY AND CONTACTED BY THE BRUSH ASSEMBLY AT SUCCESSIVE PONTS ALL SPACED FROM THE SHAFT IN A DIRECTION PERPENDICULAR TO THE SHAFT BY A DISTANCE VARYING WITH SHAFT ROTATION, THE DISTANCE VARIATION BEING A SUBSTANTIAL FRACTION OF THE MAXIMUM DISTANCE, SAID BRUSH ASSEMBLY COMPRISING A UNITARY RESILIENT ARM HAVING ONE END PORTION COMPRISING A RESISTANCE-CONTACTING SURFACE HAVING A SINGLE CONTACTING REGION AT EACH RADIAL DISTANCE FROM THE SHAFT AND OF RADIAL DIMENSION AT LEAST EQUAL TO SAID DISTANCE VARIATION CONTACTING SAID RESISTANCE ELEMENT AT POINTS ON SAID SURFACE DETERMINED SOLELY BY DISTANCE ELEMENT AT POINTS ON PORTIONS OF THE RESISTANCE ELEMENT FROM THE SHAFT, AND THE OTHER END PORTION MOUNTED ON THE SHAFT FOR ROTATION THEREWITH WHOLLY AT A POSITION SPACED FROM THE AXIS OF THE SHAFT IN THE DIRECTION GENERALLY OPPOSITE FROM THE CONTACTING END PORTION BY A DISTANCE GREATER THAN SAD RADIAL DIMENSION OF THE RESISTANCE-CONTACTING SURFACE, SO THAT VARIATION OF CONTACT PRESSURE WITH DISTANCE OF THE CONTACT POINT FROM THE SHAFT IS MINIMIZED. 